Usually a passport is asked for, contact eBay Customer Services , if all you have is the BRP documentation and that this is not being accepted, they will tell you what you need to verify your account.
To Contact Customer Services it's a Live Chat, or you can select to speak and request a Call Back. Click on this link:
https://www.ebay.co.uk/help/eua?id=5275&mkevt=1&mkpid
On weekdays lines open between 8 a.m. and 10 p.m.
On weekends they open between 9 a.m. and 6 p.m.